4 problems

Let $\gamma$ be a very long rescaled self-avoiding walk in the half-plane, let $H$ be a suitable subdomain, and let $\Phi_H$ be the conformal map used in the half-plane restriction…

Let $\mathcal{K}$ be the collection of all simply connected compact sets $K\subset\overline{\mathbbm{D}}$ such that $0\in K$ and $K\cap\mathbbm{S}^1=\{1\}$. Let $\mathcal{Q}$ be th…

Fix $\kappa\in(0,4]$, let $n\geq 1$, and let $\alpha_1,\ldots,\alpha_n$ denote the parameters of the restriction measures. Define … The generalized intersection exponents are the e…

Scaling-limit conjecture. The scaling limit of self-avoiding walk is SLE$_{8/3}$.